The author has responded to this. While he didn't deny it basically said that Kuroyukihime had a very unhappy childhood, and that isn;t something he would expect from Asuna and Kirito who are so much in love.

The link between SOA and Accel World is a crossover chapter. That's it so far.

Keep in mind that both characters from Accel World have Yuki in their names as well.

Ah interesting i actually hadn't seen his response to this and i wasn't aware of her unfortunate upbringing... while i'd still like it to be true i can see why it is now less likely

The fact both characters have Yuki in there name to me further strengthens the possibility. But again due to the comment from the author i'll admit it's unlikely.

Really how come? Reiki has said there is a link between the two 'series' no one as of yet is really sure what... Some people think Kirito is the creator of the brain burst but i think this connection would be a lot better It would put a smile on my face anyway, and you can't deny how much she looks like the two of them...

The connection could be something as simple as they are the same "universe".

NervGear was featured in Accel World. As a blurb on the internet about old virtual reality tech, but still.

The author has confirmed both series take place in the same universe that isn't up for debate

This is some points brought up by a guy by the name of Skyrius on another forum (won't mention here just incase it's against CR rules or something) but I didn't want to take his or her points without saying it was his or her ideas.

The theory about Accel World's Kuroyukihime being the daughter of Kirito and Asuna isn't too far fetched either as currently it is around 2026 or 2027 in Kirito's time which is when he is 18 years old and Asuna is 19. Accel world takes place 20 years from then in 2046. Kuroyukihime is in her 2nd/3rd year (depending where you're at) of middle school, equivalent to North America's education of 3rd year in middle school and 1st year in high school (14/15 years old). This theory is in fact VERY viable as the brain implant chip could be finished within the next 6 years (as it is stated it's being heavily and thoroughly researched on and knowing the pace of technological advances it shouldn't be too long to be in practical use, and therefore implemented from birth as a finished product) and Asuna could give birth to Kuroyukihime around that same time.

Also to those who take biology, or even those who just happen to have common sense. Kuroyukihime shares VERY similar traits to Asuna and Kirito. As I am beyond belief lazy so I will NOT post up pictures, but you are all free to do so and compare the hair (Hair is inheritable, those with a certain hair color will most likely give birth to a child with the same hair color depending on the melanin where the order is Black > Brown > Blonde > Golden Blonde > Orange (Generalizaing) ) Facial features and / or everything else.

Similarities with Kirito : Cunning attitude, wry smiles, enjoys conflict, and for god sakes her avatar is dual bladed for some reason (Though this could be coincidental). Her hair color and eye color could be considered "Pitch black as night" although it would lean to more of a purple-ish color. Favorite color? Black.

Similarities with Asuna : Very loving (Obsession with Haru), same facial structure (eyes are exaggerated but who cares), same hair structure, apparently the most attractive female in the school (Hey, in novel Asuna was easily top 5 (or even the prettiest as stated) in the world of SAO).

Its definitely a possibility, and for what i remember, it is a theory that has been flying around for some time. While i think it is chronologically possible, Kuroyukihime's past is too dark to be the child of a couple like Asuna and Kazuto, just based on their relationship, and their treatment of Yui. I do think she is somehow related or close to the two of them though. I would think it would be more likely for her to be Suguha's child, like an unwanted child or something like that before i would consider her to be the child of Asuna and Kazuto. I see those two as making great parents and having a fairly happy marriage, so to me the Princess's black past just doesnt fit.

Its definitely a possibility, and for what i remember, it is a theory that has been flying around for some time. While i think it is chronologically possible, Kuroyukihime's past is too dark to be the child of a couple like Asuna and Kazuto, just based on their relationship, and their treatment of Yui. I do think she is somehow related or close to the two of them though. I would think it would be more likely for her to be Suguha's child, like an unwanted child or something like that before i would consider her to be the child of Asuna and Kazuto. I see those two as making great parents and having a fairly happy marriage, so to me the Princess's black past just doesnt fit.

You make some fair points, I'd hate to think Asuna and Kazuto turned into bad parents.

Okay hehe so I have a few thoughts. First off the timeline matches up nearly perfectly if Kirito and Asuna were in their early twenties when they had a kid. Second Alicization isn't finished and things get very very different there, so as far as very different personalities for kirito and Asuna, well I can see this as a possibility. Third her name kuroyukihime means black snow princess. The theory here being that black being derived from her father the black swordsman, princess coming from Asuna, and my explanation for yuki, well I have no idea . We also know that her real name is not Kuroyukihime and in the anime a close friend of hers shouts out "Sacchan" at the final episode. Chan is a suffix added to a name that shows a relationship between people, by dropping this it leaves us with Sac which I believe is short for Sachi ( The girl from the moonlit black cats way back in SAO). I think she could be named this because it is a name with significance for Kirito. Other names would be either Yuuki or Yui. Yuuki is the girl in mothers rosario who has a huge impact on Asuna and Yui is their adopted virtual daughter. Yui is still around however and I don't believe if they had a daughter they would give her the same name as they would their virtual one. Anyways I do hope to see Asuna and kirito in Accel world, but i am not entirely sure if they are kuroyukihime's parents or not.

As to wether or not Alicization is finished is based on the fact that I sadly do not know much japanese and the newest light novel is not available in english yet

This could be explained if Kazuto and Asuna were in any way consciously removed from reality during Kuruyukihime's early childhood (or dead). This probably would've left her in the care of Asuna's family, who has already been established as not being the most observant group of adults in the universe (while also being particularly wealthy).

This might also explain Kuruyukihime's early desperation to reach level 10 if that in some way might save her parents.

I've only watched half of Accel World though; this might not hold water.

It'd be an interesting simultaneous reveal, though. If in a new SAO book something happens to Kazuto and Asuna, and soon after in a new Accel World book they fill you in on how that meshes with Kuruyukihime's early storyline and how that has motivated her actions (and her dark hero callousness) in Accel World up to this point.

Its definitely a possibility, and for what i remember, it is a theory that has been flying around for some time. While i think it is chronologically possible, Kuroyukihime's past is too dark to be the child of a couple like Asuna and Kazuto, just based on their relationship, and their treatment of Yui. I do think she is somehow related or close to the two of them though. I would think it would be more likely for her to be Suguha's child, like an unwanted child or something like that before i would consider her to be the child of Asuna and Kazuto. I see those two as making great parents and having a fairly happy marriage, so to me the Princess's black past just doesnt fit.

You make some fair points, I'd hate to think Asuna and Kazuto turned into bad parents.

.. So does the author of both series. He's gone on record that he has heard the rumor but based on how he wrote each of the characters he HOPED people didn't think that their marriage turned sour since her background was a sad one. If nothing else he seemed perturbed that anyone could think that. I'm sure he will address it during the rewriting of SAO that's going on now from what I gather. If nothing else it shows the inconsistencies in his writing more than anything else LOL

While I believe this theory is possible aren't all of you forgetting something important?

*SPOILERS*

In the LN for Accel World Kuroyukihime has a sister who is also one of kings called White Cosmos. She is apparently the "parent" of Kuroyukihime, meaning she was the one who introduced her to Brain Burst and made her into a burst linker. Whether or not she's older than Kuroyukihime remains to be seen, but judging from the trend shown so far in the series the "parents" who give Brain Burst to their "children" tend to at least be slightly older then them if not similar in age. If she is older than Kuroyukihime then that pokes a major whole in her being Kiritio and Asuna's child. Although, there are other possibilities that could lend credence to both theories. They could be twins whether fraternal or identical wouldn't matter but it would be an interesting angle to further explain the level of their strained relationship.

While I believe this theory is possible aren't all of you forgetting something important?

Light Novel Spoiler

Spoiler Alert! Click to show or hide

In the LN for Accel World Kuroyukihime has a sister who is also one of kings called White Cosmos. She is apparently the "parent" of Kuroyukihime, meaning she was the one who introduced her to Brain Burst and made her into a burst linker. Whether or not she's older than Kuroyukihime remains to be seen, but judging from the trend shown so far in the series the "parents" who give Brain Burst to their "children" tend to at least be slightly older then them if not similar in age. If she is older than Kuroyukihime then that pokes a major whole in her being Kiritio and Asuna's child. Although, there are other possibilities that could lend credence to both theories. They could be twins whether fraternal or identical wouldn't matter but it would be an interesting angle to further explain the level of their strained relationship.